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Option pricing with a two-piece lognormal distribution

Author

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  • Vich-Llompart, M. Magdalena
  • Vitiello, Luiz

Abstract

We derive a closed-form European option pricing model in a discrete-time utility-based setting where the underlying asset has a two-piece lognormal distribution. In our set-up, the market does not have to be dynamically complete, which makes our model applicable even in cases in which the underlying asset is illiquid. The two-piece lognormal distribution results from joining two opposite halves of two distinct lognormal distributions, where each half has a different scale parameter. Hence, it is possible to adjust the tails of the distributions to accommodate the implied volatility of in-the-money and out-of-the-money options. We show that our option pricing equation can generate several types of volatility patterns and therefore can be used to price a wide range of assets.

Suggested Citation

  • Vich-Llompart, M. Magdalena & Vitiello, Luiz, 2025. "Option pricing with a two-piece lognormal distribution," Finance Research Letters, Elsevier, vol. 85(PD).
    • Handle: RePEc:eee:finlet:v:85:y:2025:i:pd:s1544612325013753
    DOI: 10.1016/j.frl.2025.108120
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    Keywords

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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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